Factors and Multiples Game for Two

'Factors and Multiples Game for Two' printed from https://nrich.maths.org/

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Here's a game to play with an adult!

How do you play?
You'll need an adult to play with. You'll also need a grid of numbers from 1 to 100 (you can print one from here), or you can use the interactive version.

The grown-up chooses a positive even number that is less than 50, and crosses it out on the grid. You then choose another number to cross out. The number must be a factor or multiple of the first number. Take it in turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player.
The first person who is unable to cross out a number loses. Try playing again with you going first.

Do you have any winning strategies?
Are there any numbers you shouldn't go to?

Notes for grown-ups
This game can replace standard practice exercises on finding factors and multiples. In order to play strategically, pupils must start to think of numbers in terms of their factors, utilising primes and squares to develop winning moves.

Easier version: use a smaller grid, eg 1 to 50
Harder version: see what happens when the first person is allowed to choose a number greater than 50. Switch the challenge from winning the game to covering as many numbers as possible.

There's a classroom version of this game here.